Method for determining a value given to different parameters of a system

ABSTRACT

The invention relates to a method for determining a value given to the totality of specific parameters of a system using the values of the totality of measuring parameters of said system which is associated to a unit for providing with a probability value for any combination of values of the specific parameters. The inventive method consists in determining the value of each parameter and in constructing the representation of probability distribution of all possible combination of values of the specific parameters pertaining to determine values. The totality of combinations is divided into a number of first totalities of combinations. Each first totality can be divided into a number of second totalities in a similar manner and so on, a probability value being attributed to each totality. Said method also consists in selecting the totalities of values of the specific parameters using the constructed representation of probability distribution.

The present invention relates to a method for deter-mining the value tobe given to a set of so-called specific parameters of a system based onthe values of a set of so-called system measurement parameters.

Such a method may be used to control various systems such as a characterrecognition system, an electric component failure diagnosis system, asystem for evaluating a transport cost.

FIG. 1 shows an example of a system using such a method. A car 1attempts to follow a truck 2, the car and the truck being models movingon a planar obstacle-free surface. The car is equipped with a camera 3and with an autonomous control system. The control system has thefunction of defining at regular intervals, for example, every 100 ms,the direction and the speed that must be taken by car 1, as well as theinclination of the camera so that the truck permanently remains in thecamera's field of vision.

At a given time to, the control system estimates where the truck will be100 ms later, at a time t₁. In the case where the truck effectivelymoves as expected, it will be at the estimated position Pe(t₁), at thecenter of image 4 that the camera will take at time t₁. However,generally, the truck will be at a measured position Pm(t₁) differentfrom Pe(t₁). Position Pm(t₁) is shifted in the x and y direction withrespect to Pe(t₁) according to a horizontal shift c_(x) and a verticalshift c_(y). Horizontal shift c_(x) indicates whether the truck hasmoved more to the left or to the right. Vertical shift c_(y) indicateswhether the truck has accelerated or slowed down.

FIG. 2A is a side view of car 1 moving at speed v provided with camera3, and shows the vertical inclination angle α_(v) of the camera's axis.FIG. 2B is a top view of car 1, and shows horizontal inclination axisα_(h) of the camera's axis, as well as rotation angle α_(rot) of thewheels of car 1.

FIG. 3 shows a possible configuration of car 1 and of truck 2, at timet₁, truck 2 being at position Pm(t₁) of FIG. 1. The truck would thusseem to go rightwards (assumption a). The truck may also go forwards andaccelerate (assumption b). The truck may also start back off to the left(assumption c). It will be considered hereafter that the truck has butthese three possibilities and is only likely to go to one of the threeestimated positions Pe(t₂)a, Pe(t₂)b, and Pe(t₂)c.

The car control system must then decide whether the car must takedirection d₁ enabling joining truck Pe(t₂)c or whether it must takedirection d₂ enabling joining the truck at position Pe(t₂)a or Pe(t₂)c.Since the three possibilities Pe(t₂)a, Pe(t₂)b, and Pe(t₂)c are a prioriequiprobable, the selection of direction d₂ seems to be the mostjudicious since it covers a larger number of possibilities, and it willbe considered hereafter that d₂ has been selected.

The control system must then choose to increase or decrease speed v ofcar 1. The image analysis enables thinking that the truck hasaccelerated since it is at the top of the image. A first decision couldbe to require an acceleration of the car. However, the control systemhas chosen to go in direction d₂ and it is possible for the truck tosmoothly turn rightwards to reach to the position of truck Pe(t₂)a.Knowing this probability, it then seems judicious not to accelerate toomuch to avoid colliding with the truck.

The control system similarly defines angles α_(v) and α_(h) to be givento the camera according to the previously-taken decisions and to theestimate of the future displacement of the truck.

The control system of car 1 must be able to define the new values ofparameters v, α_(rot), α_(v) and α_(h), with a small-size and low-costcalculator and memory. It is further necessary for the control system totake decisions quickly, every 100 ms. The control system must alsoprocess a large number of measurement parameters c_(x), c_(y) and ofspecific or, more specifically, of control parameters v, α_(rot), α_(v),α_(h) to be able to take efficient decisions that enable following thetruck whatever its trajectory.

The forming of a control system requires previously defining theinterdependencies between parameters. Thus, in the above-describedexample, the selection of horizontal inclination angle α_(h) and ofrotation angle α_(rot) depends on the measured horizontal shift c_(x);the selection of vertical inclination angle α_(v) and the selection ofspeed v depend on the measured vertical shift c_(y). Further, angleα_(h) and angle α_(rot) are dependent from each other, otherwise thetruck risks coming out of the field of vision of the camera, whereby thecar can then no longer follow the truck. Similarly, speed v and angleα_(v) are dependent from each other, angle α_(v) having to be adapted tothe speed and vice versa.

A model of the joint probability distribution of all the systemparameters is defined based on a set of independent probabilitydistributions defined for each of the previously identifiedinterdependencies. Thus, probability p(v, α_(rot), α_(v), α_(h), c_(x),c_(y)) for a given combination of values of all the parameters to bepossible and clever, can be defined for the above-described set by thefollowing formula:p(v, α _(rot), α_(v), α_(h) , c _(x) , c _(y))=p(c _(x))p(c _(y))p(α_(h)/c _(x))p(α_(v) /c _(y))p(α_(rot)/α_(h))p(v/α _(v))  (1)where p(c_(x)) is the probability for horizontal shift c_(x) to have agiven value, p(c_(y)) is the probability for vertical shift c_(y) tohave a given value, p(ah/c_(x)) is the probability to have a horizontalinclination angle α_(h) knowing shift c_(x), p(α_(v)/c_(y)) is theprobability to have a vertical inclination angle α_(v) knowing shiftc_(y), p(α_(rot)/α_(h)) is the probability to have a rotation angleα_(rot) knowing angle α_(h), and p(v/α_(v)) is the probability to have aspeed v knowing angle α_(v).

Simple non-conditional probabilities, such as p(c_(x)), may be definedby an analytic function, for example, p(c_(x))=(absolute value ofk/c_(x)) where k is a normalization constant. Similarly, conditionalprobabilities, such as p(α_(h)/c_(x)), may be defined by a family ofanalytic functions, that may for example be gaussian functions centeredon value c_(x).

Simple probabilities, p(c_(x)), or conditional probabilities,p(α_(h)/c_(x)), can also be calculated from a database indexing thenumber of times when a horizontal shift c_(x) or a couple of values (ah,c_(x)) has been observed, for example, in a training phase.

The joint probability distribution model, the analytic functions, andthe databases are memorized. After an image has been taken at a timet_(i), the control system must decide of the value to be given to eachcontrol parameter v, α_(rot), α_(v), α_(h) based on the values noteddown for each measurement parameter at time t_(i), c_(xi), and c_(yi).The system first selects a couple of values (α_(rot), v), then, after,the other couple of values (α_(v), α_(h)). Only the selection of acouple (α_(rot), v) will be described, the selection of a couple (α_(v),α_(h)) being performed identically. Probabilityp(α_(rot),v/c_(xi),c_(yi)) for the selection of a couple (α_(rot),v) tobe pertinent knowing shift values c_(xi) and c_(yi) can be calculatedaccording to the following formula: $\begin{matrix}{{p\left( {\alpha_{rot},{v/c_{xi}},c_{yi}} \right)} = {\frac{1}{Z}{\sum\limits_{\alpha_{v},\alpha_{h}}{p\left( {v,\alpha_{rot},\alpha_{v},\alpha_{h},c_{xi},c_{yi}} \right)}}}} & (2)\end{matrix}$where Z is a normalization constant.

There are two sorts of existing control systems capable of selecting acouple (α_(rot),v) based on the probability distribution of the couples.The first ones select a couple (α_(rot),v) directly from formula (2).The second ones construct, prior to the selection of a couple(α_(rot),v), a representation of the probability distribution of thecouples.

Among the first systems, so-called optimization methods which search themaximum probability and select the corresponding couple can bementioned. Now, it may be preferable to select a couple which does notexhibit a probability maximum. For example, in the case where theprobability distribution exhibits several maximums for two couples(α_(rot,1),v₁) and (α_(rot,2),v₂), it may be pertinent to select acouple having a speed intermediary between v₁ and v₂ and a rotationangle between α_(rot,1) and α_(rot,2). Other methods such as theMETROPOLIS method (see “Monte Carlo simulation and numericalintegration” by J. Geweke, 1996), perform a random drawing of a coupledirectly from formula (2). Such methods implement calculationalgorithms, for the most part very complex and use powerful calculators.Such methods further require a significant calculation time,incompatible with certain uses such as that described in FIG. 1.

Among the second systems, certain methods use a so-called tabularrepresentation of the probability distribution. This tabularrepresentation consists of memorizing, for each couple (α_(rot),v),probability p(α_(rot),v/c_(xi),c_(yi)) obtained for the shifts c_(xi),c_(yi) measured at time t_(i). The selection of a couple may thenconsist of taking the maximum probability couple, or of performing arandom drawing of a couple from the memorized data.

In the case where the studied parameters are numerous, or when aparameter can take many values, the calculation time of theprobabilities of each couple (α_(rot),v) quickly becomes very long. Thesize of the memory used to store the tabular representation may alsoquickly become prohibitive.

A representation of the probability distribution, known as a “gaussianmixture”, consists of modeling the distribution by a set of gaussianfunctions, each gaussian function being defined from a maximumprobability value. Previously, an optimization method is used toidentify the couples (α_(rot),v) of maximum probabilities. The couplesare then distributed in groups containing more or less couples accordingto whether the couples have or not values α_(rot) and v close to theidentified maximums. A probability value is calculated for each group,the probability values forming gaussians around the maximumprobabilities. The selection of a couple is then performed by randomdrawing or search of the couple of maximum probability.

This method enables having a more or less accurate representationaccording to the available memory space. However, an increase in theaccuracy of the representation requires a new distribution of thecouples and a new calculation of the probabilities of each group.Further, the modeling of the probability distribution by a set ofgaussian functions is not adequate for all systems.

An object of the present invention is to provide a method fordetermining the values to be given to one or several specific parametersof a system knowing one or several measurement parameters, in the casewhere the number of parameters is very large and/or in the case wheresome of the parameters may take a great number of values.

Another object of the present invention is to provide a method fordetermining the values to be given to all the specific parameters of asystem within a time interval that can be very short.

Another object of the present invention is to provide such adetermination method using a memory of variable size and possibly verysmall.

Another object of the present invention is to provide such adetermination method using a simple calculation device.

To achieve these objects, the present invention provides a method fordetermining the value to be given to a set of specific parameters of asystem based on the values of a set of measurement parameters of thissystem, where each of the parameters can take a finite number of values,the system being associated with a means for providing a probabilityvalue for any combination of values of the specific parameters, saidprobability value being all the greater as the selection of theconsidered combination is pertinent knowing the value of the measurementparameters, the method comprising the steps of:

-   -   noting down the value of each measurement parameter;    -   constructing a tree-shaped representation of the probability        distribution of all the possible combinations of values of the        specific parameters corresponding to the noted down values, the        set of combinations, forming a first branch, being divided into        several subsets of combinations, forming second branches, each        subset gathering combinations having close specific parameter        values, where each second branch can similarly divide into        several third branches and so on, a probability value being        assigned to each branch, this probability value being that        obtained for one of the combinations of the considered branch or        for one of the combinations of one of the branches from which        the considered branch originates;    -   selecting according to a predefined selection criterion one of        the combinations of values of the specific parameters based on        the representation of the previously-constructed tree-shaped        probability distribution.

According to an implementation mode of such a method, the branchesresulting from the division of a same branch are at the number of twoand contain the same number of combinations, the first branch dividingin two second branches, where each second branch can divide in two thirdbranches and so on.

According to an implementation mode of such a method, the division of abranch in two branches comprises the steps of:

-   -   a) selecting a combination different from the combinations        having already been used to define the probability value of the        existing branches and calculating the probability of this        selected combination;    -   b) dividing the so-called “parent” branch containing the        selected combination in two so-called “child” branches; and    -   in the case where the selected combination and the “parent”        combination used to define the probability value of the parent        branch belong to the same child branch, assigning to the two        child branches the probability value of the parent branch and        dividing the child branch containing the selected combination by        resuming the method at step b), this child branch becoming the        parent branch, and    -   in the case where the selected combination and the parent        combination do not belong to the same child branch, assigning        the probability value of the selected combination to the child        branch containing the selected combination and assigning the        probability value of the parent combination to the other child        branch.

According to an implementation mode of such a method, the selectioncriterion consists of selecting one of the combinations exhibiting themaximum probability.

According to an implementation mode of such a method, the selection of acombination consists of implementing the recursive method comprising thesteps of:

-   -   a) randomly selecting a number p ranging between 0 and 1;    -   b) calculating the sum of the probability values assigned to the        two so-called child branches resulting from the division of the        first branch, and calculating for each child branch a new        probability value equal to the ratio between the probability        value assigned to this child branch and the calculated sum;    -   c) defining two contiguous probability intervals between 0 and        1, the first interval being associated with a first child        branch, the second interval being associated with the second        child branch, the first interval ranging from 0 to and including        the probability value of the first child branch and the second        interval ranging from this probability value to 1;    -   d) identifying in which interval number p is to be found and        selecting the child branch associated with this interval, and    -   in the case where the selected child branch ramifies into other        branches, resuming the recursive method at step a), the first        branch being replaced with the selected child branch, otherwise    -   e) selecting one of the combinations of the selected child        branch.

According to an implementation mode of such a method, the selectioncriterion consists of selecting one of the combinations having aprobability value which is predetermined or ranging between two givenprobability values.

According to an implementation mode of such a method, the probabilityvalues assigned to each branch are not normalized and can be greaterthan one.

According to an implementation mode of the above-described method, aweighting is assigned to each branch, the weighting of the branches ofthe last ramifications being equal to the product of the probabilityvalue assigned to this branch and of the number of combinations of thisbranch, the weighting of the other branches being equal to the sum ofthe weightings of the branches originating from the considered branchand being on the next ramification level.

According to an implementation mode of the above-described method, theprobability value assigned to each branch can be normalized, thenormalized probability value of a branch being obtained by dividing theprobability value of this branch by the weighting assigned to the firstbranch of the tree.

According to an implementation mode of such a method, the selection of acombination is performed by implementing a method generatingcombinations having high probability values.

According to an implementation mode of such a method, the representationof the probability distribution of all the combinations is memorized andmay be subsequently refined by the creation of additional branches, ormay be simplified by the suppression of certain branches.

According to an implementation mode of such a method, the number ofvalues likely to be taken by a parameter is artificially increased, theprobability value of a combination of values of control parameters,among which at least a value of one of the parameters corresponds to anadded value, is zero.

The foregoing objects, features, and advantages of the present inventionwill be discussed in detail in the following non-limiting description ofspecific embodiments in connection with the accompanying drawings, amongwhich:

FIG. 1 shows a car attempting to follow a truck;

FIG. 2A illustrates a side view of the car of FIG. 1;

FIG. 2B illustrates a top view of the car of FIG. 1;

FIG. 3 illustrates a possible configuration of the car and of the truckas well as three future possible positions of the truck;

FIGS. 4A to 4G illustrate steps of a method according to the presentinvention of construction of a representation of a probabilitydistribution;

FIG. 5 illustrates in the form of a ramified tree the steps of FIGS. 4Bto 4G;

FIGS. 6A to 6D illustrate two possible division modes of the set ofcouples (α_(v),α_(h)) according to the method of the present invention;

FIG. 7 illustrates an application of the method of the present inventionto the failure diagnosis of an electric component assembly; and

FIG. 8 illustrates an application of the method of the present inventionto the recognition of figures.

The method of the present invention applies to any system definedaccording to the criteria discussed hereafter. It can be decided of thevalue to be given to n specific parameters XS₁ to XS_(n) of the system,knowing the values of n measurement parameters XM₁ to XM_(m)corresponding to a determined state of the system. Each of theparameters can take a finite number of values. The values of thespecific parameters form a continuous sequence of integers. Themeasurement parameters may be symbolic variables, where the possiblevalues can be yellow, blue, green, and red. A model of the jointprobability distribution of the set of system parameters is known andthe probability p(XS₁, . . . , XS_(n),XM, . . . ,XM_(m)) for a givencombination of all the parameters (XS₁, . . . ,XS_(n),XM₁, . . .,XM_(m)) to be pertinent is calculated. The analytic functions and thedatabases used by the probability distribution model of the system areknown.

At any time, it is possible to make from the system model an inferenceconsisting of defining the probability distribution of the combinationsof values of all or part of the specific parameters, for example(XS₁,XS₂,XS_(n)), knowing the values of all or part of the measurementparameters, for example, (XM₁,XM₃). Probabilityp(XS₁,XS₂,XS_(n)/XM₁,XM₃) for the selection of a combination(XS₁,XS₂,XS_(n)) to be pertinent knowing the values of measurementparameters (XM₁,XM₃) is defined by: $\begin{matrix}{{p\left( {{XS}_{1},{XS}_{2},{{XS}_{n}/{XM}_{1}},{XM}_{3}} \right)} = {\frac{1}{Z}{\sum\limits_{\substack{{XS}_{3},\ldots\quad,{XS}_{n - 1}, \\ {XM}_{2},{XM}_{4},{\ldots\quad{XM}_{m}}}}{p\left( {{XS}_{1},\ldots\quad,{XS}_{n},{XM}_{1},\ldots\quad,{XM}_{m}} \right)}}}} & (3)\end{matrix}$where Z is a normalization constant.

After noting down the considered measurement parameters, the presentinvention provides a method for constructing a representation of theprobability distribution of the combinations of the values of the kselected specific parameters, obtained for the noted down values. Acombination of values of the k selected parameters will be called “acombination” hereafter. The set of combinations may be represented by aset of points defined in a k-dimensional space E. The probabilitydistribution is then represented in a k+1-dimensional space.

The construction method of the present invention aims at dividing spaceE into several sets of points and at assigning an identical probabilityvalue to all the points of a same set to obtain a representation of theprobability distribution of the combinations.

Once the representation of the probability distribution of thecombinations has been obtained by the method of the present invention,the selection of a combination is performed according to one of severalselection criteria.

There can be a great variety of applications of the method of thepresent invention, as will appear from the reading of the mentionedexamples.

In a first part, a method for constructing a representation of theprobability distribution of the combinations will be described.

In a second part, different selection criteria will be described.

In a third part, examples of application of the method of the presentinvention will be described.

1. Construction Method

1.1. General Principle

The method for constructing a representation of the probabilitydistribution of the combinations consists of successively selectingdifferent combinations from among the set of possible combinations andof calculating their respective probability values. After each selectionof a combination, the set of points of space E containing the selectedcombination is divided into several sets of points. The set of pointscontaining the selected combination takes the probability value of thiscombination. The other sets of points keep the probability value thatthey had before the division.

Initially, space E is not divided and all the points of space E takeprobability value p₁ of the first selected combination C₁.

The selection of a second combination C₂, different from the firstselected combination C₁, causes a division of space E into several setsof points, the set of points containing the second selected combinationC₂ taking probability value p₂ of the second selected combination C₂,the other sets of points taking probability value p₁ of the firstselected combination C₁.

The selection of a third combination C₃, different from the first andsecond selected combinations C₁ and C₂, causes the division of the setof “parent” points containing the third selected combination C₃ intoseveral sets of “child” points containing the third selected combinationC₃ taking probability value p₃ of the third selected combination, theother sets of “child” points taking the probability value of the set of“parent” points, p₁ or p₂.

The selection of a possible fourth combination C₄, different from thoseselected previously, would cause a new division of the set of “parent”points containing the fourth selected combination C₄ into several setsof “child” points, the set of “child” points containing the fourthselected combination C₄ would then take probability value p₄ of thefourth selected combination C₄, and the other sets of “child” pointswould take the probability value of the set of “parent” points p₁, p₂,or p₃.

This construction method can be repeated as many times as possibleaccording to the available time. The representation of the probabilitydistribution will be all the more accurate as the number of selectedcombinations is large. Conversely to the creation of a representationaccording to the “gaussian mixture” method, the construction method ofthe present invention can be executed for a variable time, where theselection of the execution time can be adapted to each system.

The successively-selected combinations can be obtained according to apseudo-random method generating combinations uniformly distributed overspace E or according to an optimized method generating combinationshaving high probability values.

According to an implementation mode of the method of the presentinvention, each set of “child” points, resulting from the division of aset of “parent” points, comprises an identical number of combinations.

1.2. Construction Tree

The present invention provides keeping a trace of the construction ofthe probability distribution via a construction tree.

The first branch of the construction tree represents space E and takesprobability value p₁ The first branch ramifies into second branches eachrepresenting one of the sets of points resulting from the division ofspace E. Each second branch takes the probability value of the points ofthe second considered branch.

The second branch associated with the set of “parent” points containingthe third selected combination C₃ ramifies into third branches eachrepresenting one of the sets of “child” points. Each third branch takesthe probability value of the points of the third considered branch.

Generally, each second branch is likely to ramify into several thirdbranches according to the new selected combinations. Each third branchcan ramify into several fourth branches and so on.

The construction tree is memorized along its construction. The endbranches of the tree give the final division of the set of combinations.The final representation of the probability distribution will be usedhereafter to select one of the combinations, as will be described in thesecond portion. It may be provided to construct a representation of theprobability distribution which is more or less accurate according to theavailable memory.

The creation of a construction tree has several advantage, as will bespecified hereafter, especially for the obtaining of normalizedprobability values and for the selection of a combination by randomdrawing according to a random drawing method of the present invention.

1.3. Illustration for the Car/Truck System

1.3.1 Selection of a Speed

The construction of a representation of the probability distribution ofthe combinations according to the method of the present invention isillustrated hereafter for the previously-described car/truck system.

The case where the car control system decides of the values to be givento control parameters (α_(rot), v, α_(v), α_(h)) one after the others isfirst considered. In the case of a speed selection, probability p(v) forthe selection of a speed v at a time t_(i) to be pertinent, knowingshift values c_(xi) and c_(yi) noted down at time t_(i), can becalculated as follows:${p\left( {{v/c_{xi}},c_{yi}} \right)} = {\frac{1}{Z}{\sum\limits_{\alpha_{v},\alpha_{h},\alpha_{rot}}{p\left( {v,\alpha_{rot},\alpha_{v},\alpha_{h},c_{xi},c_{yi}} \right)}}}$

FIG. 4A shows a probability distribution 10 of the speed values obtainedfor shift values c_(x0) and c_(y0) noted down at time t₀. Thisdistribution is that of which an approximation is desired to beobtained, simply, rapidly, and minimizing the used calculation andmemorization means. Speed v may take an integral value ranging betweenand including 0 and 15 km/hour. The speed is shown in abscissas,probability p(v) is shown in ordinates. In this example, probabilitydistribution 10 of the speed values is a continuous function which is 0when the speed is zero or greater than 14 and which exhibits two maximumvalues for speeds v equal to 4 km/h and 10 km/h.

FIGS. 4B to 4G altogether illustrate the construction of arepresentation of the probability distribution of FIG. 4A. The sets ofspeed values, or branches, are shown by a two-way arrow positioned underthe speed values belonging to the branch. A horizontal line cuttingprobability distribution 10, and placed above a two-way arrow, shows theprobability value associated with the speed values of the branch shownby the two-way arrow.

FIG. 4B illustrates a first step of the construction linked to theselection of a first speed value v₁ equal to 4 km/h of probability p₁,where the set of speed values, forming a first branch B, takesprobability value p₁.

FIG. 4C illustrates a second step of the construction linked to theselection of a second speed value v₂ equal to 12 km/h, of probabilityp₂. The set of speed values is divided in two sets of speed valuesforming each of second branches B₁ and B₂. Branch B₁ gathers thesmallest speed values ranging from 0 to 7 km/h. Branch B₂ gathers thehighest speed values ranging from 8 to 15 km/h. The two branches B₁ andB₂ gather a same number of speed values. Branch B₂ contains the secondselected speed value v₂, it thus takes probability value p₂. Branch B₁keeps probability value p₁.

According to a first aspect of the implementation mode of the method ofthe present invention selected for this example, the ramification of abranch results in the creation of two branches comprising a same numberof speed values, one of the branches comprising the smallest speedvalues, the other branch comprising the highest speed values.

FIGS. 4D and 4E illustrate two phases of a third step of theconstruction linked to the selection of a third speed value v₃ equal to6 km/h of probability value p₃. In a first phase, branch B₁ containingthe third selected speed value v₃ ramifies in two branches B_(1,1) andB_(1,2) as appears in FIG. 4D. Branch B_(1,1) gathers the speed valuesranging from 0 to 3 km/h, branch B₁, ₂ gathers the speed values rangingfrom 4 to 7 km/h. The first and third selected speed values v₁ and v₃belong to the same branch B_(1,2). In this case, branches B_(1,1) andB_(1,2) keep probability value p₁ The ramification method will carry on(FIG. 4E) until one of the branches only contains the third speed valuev₃.

According to a second aspect of the implementation mode of the method ofthe present invention selected for this example, the ramification of a“parent” branch containing the last selected speed value carries onuntil a “child” branch only contains the new selected speed value and noother previously-selected speed value. The intermediary “child” branchestake the probability value of the “parent” branch.

FIG. 4E illustrates the second phase of the third step. Branch B_(1,2)containing the third selected speed value v₃ thus ramifies in twobranches B_(1,2,1) and B_(1,2,2) respectively comprising speed values4.5 and 6.7 km/h. Branch B_(1,2,2) only contains the third selectedspeed value v₃ and no other selected speed value. Probability value p₃is thus assigned to branch B_(1,2,2). Branch B_(1,2,1) keeps probabilityvalue p₁ of branch B_(1,2) from which it originates.

FIG. 4F illustrates a fourth step of the construction linked to theselection of a fourth speed value v₄ equal to 10 km/h of probabilityvalue p₄. Branch B₂ containing the fourth selected speed value v₄ramifies in two branches B_(2,1) and B_(2,2), the branches respectivelygathering speed values 8 to 11 and 12 to 15 km/h. The fourth speed valuev₄ belongs to branch B_(2,1) and no other selected speed value belongsto this branch. Probability value p₄ is then assigned to branch B_(2,1).Branch B_(2,2) keeps probability value p₂.

FIG. 4G illustrates a fifth step of the construction linked to theselection of a fifth speed value v₅ equal to 1 km/h, of probability p₁.Branch B_(1,1) containing the fifth selected speed value v₅ ramifies intwo branches B_(1,1,1) and B_(1,1,2) the branches respectively gatheringspeed values 0, 1 and 2, 3 km/h. The fifth selected speed value v₅ onlybelongs to branch B_(1,1,1) and no other selected speed value belongs tothis branch. Probability value p₅ is then assigned to branch B_(1,1,1).Branch B_(1,1,2) keeps probability value p₁. It should be noted that atthis last stage, a good approximation of probability distribution 10 ofFIG. 4A has been obtained.

FIG. 5 shows the construction tree of the representation of theprobability distribution of the speed values obtained according to thefive steps described in relation with FIGS. 4A to 4G. Branch B ofprobability value p₁ ramifies in two branches B₁ and B₂ of respectiveprobability values p₁ and p₂. Branch B₂ ramifies in two branches B_(2,1)and B_(2,2) of respective probabilities p₁ and p₂. Branch B₁ ramifies intwo branches B_(1,1) and B_(1,2) of probability value p₁ Branch B_(1,1)ramifies in two branches B_(1,1,1) and B_(1,1,2) of respectiveprobability values p₅ and p₁. Branch B_(1,2) ramifies in two branchesB_(1,2,1) and B_(1,2,2) of respective probability values p₁ and p₃. Thefinal division of the set of speed values is provided by the endbranches of the construction tree.

1.3.2. Selection of Angles (α_(h),α_(v))

The construction of a representation of the probability distribution ofthe combinations according to the method of the present invention isillustrated hereafter in the case where the car control system decidesof the values to be given to two control parameters.

FIGS. 6A to 6D show the two-dimensional space E of all the couples ofvalues of horizontal and vertical inclination angles (α_(h),α_(v)). Acouple of horizontal and vertical inclination angles (α_(h),α_(v)) willbe called a couple hereafter. Horizontal inclination angle α_(h) isshown in abscissas. Vertical inclination angle α_(v) is shown inordinates.

Probability p(α_(h),α_(v)/c_(xi),c_(yi)) for the selection of a couple(α_(h),α_(v)) to be pertinent knowing shift values c_(xi) and c_(yi) canbe calculated according to the following formula: $\begin{matrix}{{p\left( {\alpha_{h},{\alpha_{v}/c_{xi}},c_{yi}} \right)} = {\frac{1}{Z}{\sum\limits_{\alpha_{rot},v}{p\left( {v,\alpha_{rot},\alpha_{v},\alpha_{h},c_{xi},c_{yi}} \right)}}}} & (4)\end{matrix}$where Z is a normalization constant andp(v,α_(rot),α_(v),α_(h),c_(x),c_(y)) is calculated according to formula(1).

The implementation mode of the method of the present invention for thisexample uses the first and second above-described aspects. The branchesresulting from a ramification are at the number of two and contain thesame number of couples. The ramification of a branch carries on untilthe last selected couple is the only selected couple of one of thebranches.

Horizontal inclination angle α_(h) can take six values between 0° and5°, vertical inclination angle α_(v) can take four values between 0° and3°.

To simplify the computer processing, the number of values likely to betaken by a parameter, if it is not a power of two, is increased to theimmediately greater power of two. The probability of the couples havingone of their parameters corresponding to an added value (not initiallyprovided) is zero.

In this example, horizontal inclination angle α_(h) can initially takesix values. The number of values is thus artificially brought to 8 (2³),and the possible values now are from 0° to 7°. No increase in the numberof values is performed for vertical inclination angle α_(v) for which 4(2²) values are possible.

FIG. 6A shows the set of couples (α_(h),α_(v)) forming first branch B.As previously, a first couple C₁ (α_(h1)=2, α_(v1)=3) and theprobability value p₁ calculated for the first couple C₁ is assigned toall the couples of branch B.

FIG. 6B illustrates a possible ramification of branch B after selectionof a second couple C₂ (α_(h2)=7, α_(v2)=4) of probability p₂. Branch Bramifies in two branches B₁ and B₂ according to a vertical limit 12passing between horizontal inclination angle values 3° and 4°. Branch B₁gathers the couples having a horizontal inclination angle strictlysmaller than 4 (2²). Branch B₂ gathers the couples having a horizontalinclination angle greater than 4 (2²).

According to an aspect of the implementation mode of the method of thepresent invention for this example, the ramification of a “parent”branch results in the creation of two branches according to a verticallimit. In the case where it is impossible to define a vertical limit,that is, when the couples of the “parent” branch all have the samehorizontal inclination value α_(h), the division is performed accordingto a horizontal limit passing between two vertical inclination valuesα_(v).

FIGS. 6C and 6D illustrate another possible ramification of branch B,the second selected couple C_(2′) (α_(v2′)=1, α_(h2′)=1) being differentfrom C₂. FIG. 6C illustrates a first division of branch B according tothe same vertical limit 12 as that previously defined. The selectedfirst couple C₁ and second couple C_(2′) both belong to branch B₁.Branches B₁ and B₂ take probability value p₁ of first couple C₁ and anew ramification of branch B₁ containing couple C_(2′) is performeduntil the two selected couples C₁ and C_(2′) are in different branches.

FIG. 6D illustrates the ramification of branch B₁ according to ahorizontal limit 13 passing between values 1° and 2° of verticalinclination angle α_(v). Branch B_(1,1) gathers the couples having avertical inclination angle value greater than or equal to 2. BranchB_(1,2) gathers the couples having a vertical inclination value strictlysmaller than 2. Branch B_(1,2) take probability value p₂ of secondcouple C_(2′) and branch B_(2,2) takes probability value p₁.

According to another aspect of the implementation mode of the method ofthe present invention for this example, the successive ramifications ofa “parent” branch are successively performed according to a verticallimit and a horizontal limit until the new selected combination is theonly one of the selected combinations to belong to a given “child”branch.

1.4. Normalized Probability Values

The probability values, for example p(XS₁, XS₂, XS_(n)), obtained fromformula (3) are in fact defined to within a constant, normalizationconstant Z. This constant can be calculated only when the probabilityvalues of all combinations (XS₁, XS₂, XS_(n)) are known and have beencalculated without taking Z into account (Z taken to be equal to 1).Normalization constant Z is then equal to the sum of all the probabilityvalues.

In practice, only very few probability values are calculated onconstruction of the representation of the probability distribution. Theprobability values calculated for the selected combinations are notnormalized.

The present invention provides defining an intermediary normalizationconstant Zi which is an estimate of normalization constant Z.Normalization constant Zi is calculated during the construction of theprobability distribution representation. It is equal to the sum of theprobability values of all combinations, the probability value of acombination being that assigned to the branch containing the consideredcombination.

To easily calculate intermediary normalization constant Zi, the presentinvention provides assigning a weight to each branch. The weighting ofthe branches of the last ramification is equal to the product of theprobability value associated to the considered branch and of the numberof combinations of this branch. The weighting of the other branches isequal to the sum of the weightings of the branches originating from theconsidered branch and located on the next ramification level. Theweighting of the first branch is then equal to intermediarynormalization constant Zi.

The weightings are updated on ramification of one of the end branches ofthe construction tree. The weightings of the branches located betweenthe first branch and the ramifying end branch must be recalculated.

Thus, for the example of construction of the speed probabilitydistribution representation shown in FIGS. 4B to 4G, the weighting ofbranch B₁ at the end of the first step, FIG. 4B, is 16*p₁. At the end ofthe second step, FIG. 4C, the weightings of the new branches B₁ and B₂respectively are 8*p₁ and 8*p₂, and the weighting of branch B is updatedand now is 8*p₁+8*p₂. At the end of the third step, FIG. 4D, theweightings of branches B_(1,1) and B_(1,2) both are 4*p₁, and theweighting of branches B₁ and B remains unchanged (respectively4*p₁+4*p₁=8*p₁ and (4*p₁+4*p₁)+8*p₁=16*p₁) since the probability valuesassigned to the different speeds have not changed, only the division ofthe speed values having changed. At the end of the fourth step, FIG. 4E,the weightings of branches B_(1,2,1) and B_(1,2,2) respectively are 2*p₁and 2*p₃, the weighting of branch B_(1,2) now is 2*p₁+2*p₃, theweighting of branch B₁ is 4*p₁+(2*p₁+2*p₃) and the weighting of branch Bis (4*p₁+(2*p₁+2*p₃))+8*p₂. An advantage of the method of the presentinvention is that it enables rapidly knowing the normalized probabilityvalue of the speed since it is not necessary to calculate all theprobability values.

1.5. Advantages

The method of the present invention enables representing a great varietyof probability distributions, conversely to the so-called “gaussianmixture” method.

The method of the present invention enables obtaining a more or lessdetailed representation according to the available memory and to theallowed calculation time.

Further, the implementation of an optimized method for the combinationselection enables obtaining within a very short time a representationtaking up little memory and exhibiting a sufficient accuracy for theareas of space E where the combinations exhibit high probability values.The method of the present invention thus is “multi-resolution” in thatthe division of space E can be very fine for certain portions and roughfor others.

This “multi-resolution” feature of the method of the present inventionenables, conversely to existing representations, constructing within arelatively short time and by using memories of reasonable size,probability distribution representations of a large number of controlparameters or parameters that can take a large number of values.

2. Selection

Known modes of selection of one of the combinations based on arepresentation of the probability distribution of the combinationsconsist of selecting one of the combinations exhibiting the maximumprobability or of selecting a combination by random drawing, theprinciple of which will be recalled hereafter. Other selection criteriasuch as the selection of the one of the combinations having apredetermined probability value or the selection of one of thecombinations having a probability value ranging between two givenprobability values may however be defined.

2.1. Selection of a Combination of Maximum Probability

According to an implementation mode of the method of the presentinvention, a memory register is used to store an indication of thebranch(es) exhibiting the maximum probability value. The registerinitially memorizes the first branch of the construction tree, afterwhich it is updated during the construction of the probabilitydistribution representation. At each ramification of a branch, it ischecked whether the probability value of the last selected combinationis greater than the probability value of the branch memorized by theregister, and if such is the case, the register is updated and memorizesthe new branch containing the last selected combination.

In the case where the branch of maximum probability ramifies and givesone or several “child” branches of same probability, the register isupdated and memorizes all the “child” branches.

The selection of a combination then consists of identifying the branchmemorized by the register containing the greater number of combinationsand of then selecting one of the combinations of this branch.

2.2. Selection by Random Drawing

A random drawing consists of selecting one of the possible combinationsin a way such that a combination exhibiting a high probability stands ina good chance of being selected and a combination exhibiting a lowprobability stands in a poor chance of being selected. After a greatnumber of random drawings, the probability distribution of the “drawn”combinations is identical to the probability distribution of the initialcombinations on which the random drawing method is based.

According to an implementation mode of the method of the presentinvention, the random drawing of a combination is performed according toa recursive selection method using the construction tree of therepresentation of the probability distribution.

Starting from the first branch, a second branch, then a third branch areselected, and so on until an end branch of the construction tree isselected. For this purpose, a second branch is selected by performing arandom drawing from among the second branches. The second branchesexhibiting the highest probabilities stand in the best chance of beingselected, and conversely. One of the third branches originating from theselected second branch is similarly selected by performing a randomdrawing between these third branches, and so on.

In the case where each branch ramifies in two branches, the method ofthe present invention comprises several steps described hereafter.

In a first step of the method, a number p ranging between 0 and 1included is randomly selected.

In a second step, sum S of the probability values assigned to the 2“child” branches resulting from the ramification of the first branch iscalculated. Then, for each “child” branch, a new probability value equalto the ratio between the probability value assigned to the consideredbranch and the calculated sum S is calculated.

In a third step, two contiguous probability intervals are definedbetween 0 and 1, the first interval being associated with a first childbranch, the second interval being associated with the second childbranch. The first interval ranges from 0 to and including theprobability value of the first child branch and the second intervalranges from this probability value to 1.

In a fourth step, it is identified in which interval number p is locatedand the “child” branch associated with this interval is selected.

In the case where the selected “child” branch ramifies in otherbranches, the recursive method is resumed at the first step, the firstbranch being replaced with the selected “child” branch. The firstselected number p may be used again.

In the case where the selected “child” branch does not ramify into otherbranches, the recursive method stops and one of the combinations of theselected child branch is selected.

The above-mentioned recursive selection method is used in the example ofthe car/truck system to select a speed or a couple of inclination angles(α_(v),α_(h)).

An advantage of the method of the present invention is that the randomdrawing method is simple and easy to implement.

2.3. Tree Memorization

Once the decision has been taken, the construction tree can be erasedfrom the memory. It may however be provided, for systems such as the carand the truck, to keep in a “cache” memory the construction treessuccessively obtained after different samplings of the measurementparameters. The most often used construction trees may be memorized.

In the case where a probability distribution is often used, itsrepresentation can be refined by carrying on the ramification of theconstruction tree of this representation. In the car/truck example, thetree ramification may be carried on for the time allowed between thesampling of the values of c_(x) and c_(y) and the time when the valuesof α_(rot), v, α_(v), and α_(h) must be selected.

Similarly, in the case where a probability distribution has been muchused at a given time, and less afterwards, the accuracy of theprobability distribution can be decreased by suppressing more or lessend branches of the construction tree.

In the case where it is chosen to calculate a weighting for each branchto know the intermediary normalization constant such as definedhereabove, the weighting values of the branches located between thefirst branch and the suppressed branch(es) will be updated.

An advantage of the method of the present invention is that it enablesrefining or simplifying a probability distribution representation. Thisenables implementing strategies of memorization of different probabilitydistributions to globally improve the successive combinationsselections.

3. EXAMPLES OF APPLICATION

3.1. Failure Diagnosis

FIG. 7 shows an electric device that comprises several componentsbetween an input I and an output O, each component being capable ofconducting part of input current K when operating, with no currentflowing when the component is defective.

A component A is placed between input I and a first intermediary point100. Output current KA of component A is equal to 100% of current K whenthe component operates (and equal to 06 of current K when the componentis defective).

Components B and C are placed in parallel between first intermediarypoint 100 and a second intermediary point 101. Output current KB ofcomponent B is at most equal to 40% of current K when component Boperates.

Component C is formed of two components C₁ and C₂ in parallel. Eachcomponent C₁ and C₂ can conduct up to 30% of current K. Output currentKC of component C may thus be equal to 0%, 30%, or 60% of current K,according to whether the two components are defective or the twocomponents are operative.

A component D is placed between point 101 and output O. Component D isformed of eight components D₁ to D₈ in parallel. Each component D₁ to D₈can conduct up to 15% of current K when it operates. Further, it isnecessary that at least six of components D₁ to D₈ operate for componentD to operate.

Current KBC entering component D is equal to the sum of current KB andof current KC. Current KBC may be equal to 0%, 30% (only C₁ or C₂ isoperative), 40% (only B operates), 60% (C₁ and C₂ are operative), 706(C₁ or C₂ and B are operative) or 100% (C₁, C₂, and B operate) ofcurrent K.

Output current KD of component D may be equal to 0%, 30%, 40%, 60%, 70%(KBC is respectively equal to 0%, 30%, 40%, 60%, and 70% of current Kand at least six of components D₁ to D₈ are operative), 90% (KBC isequal to 100% of current K and 6 components D₁ to D₈ are operative) or100% (KBC is equal to 100% of current K and at least 7 components D₁ toD₈ are operative) or current K.

Each component A, B, C₁, C₂ and D₁ to D₈ can be considered as being aparameter of the device that can take value 0 when the component isdefective, and 1 when the component is operative. Output currents KA,KB, KC, KBC, and KD are also considered as being parameters of thedevice that can take more or less values. Thus, KA and KB can take value0 or 1 according to whether the current is respectively 0% or 100% ofcurrent K. KC can take values 0, 1, or 2 according to whether thecurrent respectively is 0%, 30%, or 60% or current K. KBC can takevalues 0, 1, 2, 3, 4, or 5 according to whether the current respectivelyamounts to 0, 30, 40, 60, 70, or 100% of current K. KD can take values 0to 7 according to whether the current respectively is 0, 30, 40, 60, 70,90, or 100% of current K.

Probability p(A,B,C₁,C₂,D₁, . . . ,D₈,KA,KB,KC,KBC,KD) for a givencombination of all parameters to be pertinent is defined as follows:p(A,B,C ₁ ,C ₂ ,D ₁ , . . . ,D ₈ ,KA,KB,KC,KBC,KD)=p(A)p(B)p(C ₁)p(C₂)p(D ₁)p(D ₂)p(D ₃)p(D ₄)p(D ₅)p(D ₆)p(D ₇)p(D ₈)p(KA)p(KB)p(KC)p(KBC)p(KD)p(KA/A)p(KB/B,KA)p(KC/C,KA)p(KBC/KB,KC)p(KD/KBC,D)  (4)where

-   p(A), p(B), p(C₁), p(C₂), p(D₁) to p(D₈), p(KA), p(KB), p(KC),    p(KBC), and p(KD) respectively are the probabilities for A, B, C₁,    C₂, KA, KB, KC, KBC, and KE to have a given value,-   p(KA/A) is the probability for KA to have a given value knowing the    value of A,-   p(KB/B,KA) is the probability for KB to have a given value knowing    the value of B and of KA,-   p(KC/C,KA) is the probability for KC to have a given value knowing    the value of C and of KA,-   p(KBC/KB,KC) is the probability for KBC to have a given value    knowing the value of KB and of KC,-   p(KD/KBC,D) is the probability for KD to have a given value knowing    the value of KBC and of D.

Simple probabilities p(A) to p(KD) can be defined from databases notingdown the failure cases having appeared in tests performed by the firmmanufacturing the device. Conditional probabilities p(KA/A) top(KD/KBC,D) can easily be defined based on the device description. Forexample:p(KA=0%/A=0)=1p(KA=100%/A=0)=0p(KA=0%/A=1)=0p(KA=100%/A=1)=1

In a failure diagnosis of the device, the current at a point of thedevice (KA, KB, KC, KBC, or KD) can be measured and/or the operatingstate of one or several components of the device (A, B, C₁, C₂, D₁ toD₈) can be considered. Once one or several currents have been sampledand/or one or several components have been analyzed, it can bedetermined which components are likely to fail (diagnosis 1) or whatcurrent is likely to flow at a point of the device (diagnosis 2).

According to the performed diagnosis, parameters A, B, C₁, C₂, D₁ to D₈,KA, KB, KC, KBC, and KC can be either specific parameters, the value ofwhich is desired to be determined, or measurement parameters, since thecurrent or the operating state is measured, or non-retained parameterssince their value is not desired to be determined and their value is notmeasured.

In diagnosis 1, the measurement parameters are one or several currents,for example, KBC, and the specific parameters are one or severalcomponents, in this example, components A, B, C₁, and C₂ locatedupstream of current KBC. After a sampling of the value of current KBC, arepresentation of the probability distribution of the combinations ofvalues of parameters A, B, C₁, and C₂ is constructed according to themethod of the present invention, knowing the value of measurementparameter KBC. Probability p(A,B,C₁,C₂/KBC) for a combination(A,B,C₁,C₂) to represent the state of the device, knowing the value ofKBC, can be calculated as previously by summing up all the probabilitiesp(A,B,C₁,C₂,D₁, . . . ,D₈,KA,KB,KC,KBC,KE) for all the parameter valuesnot retained in this inference (D₁ to D₈, KA, KB, KC, KD). It will befirst desired to identify a first combination, that exhibiting themaximum probability, to perform a first repair. If this repair appearsto be insufficient or unfounded, a second combination exhibiting thehighest probability after the first combination will be identified, andso on.

In diagnosis 2, the control parameter will be the current which isdesired to be known, for example, KBC, where the measurement parametersmay be one or several of the other parameters. After a sampling of thevalue of the measurement parameters, a representation of the probabilitydistribution of the possible values of current KBC will be constructedaccording to the method of the present invention. The value of currentKBC exhibiting the maximum probability is then selected.

3.2. Figure Recognition

FIG. 8 shows an image 200 of a figure written by hand which is desiredto be identified. The image is broken down into 64 squares or pixels ofidentical sizes. For each pixel, a grey level representing the surfacearea taken up by the lines of the figure in the considered pixel ismeasured on a scale from 0 to 16.

The system comprises a single parameter to be determined (or specificparameter) CHIFFRE that can take values 0 to 9 and 64 measurementparameters Pix[i], i being an integer ranging between 1 and 64, that caneach take values 0 to 15.

Probability p(CHIFFRE,Pix[1], . . . ,Pix[64]) for a given combination ofvalues of all the parameters to be possible, is defined as follows:p(CHIFFRE,Pix[1], . . . ,Pix[64])=p(CHIFFRE)*p(Pix[1]/CHIFFRE)* . . .p(Pix[64]/CHIFFRE)  (5)where p(CHIFFRE) is the probability to have a given figure, andp(Pix[i]/CHIFFRE) is the probability to have a given grey level forpixel Pix[i], knowing the figure.

It is generally considered that FIGS. 0 to 9 are equiprobable and thusthat p(CHIFFRE) is equal to 1/10. Conditional probabilitiesp(Pix[i]/CHIFFRE) are defined at the end of a training phase consistingof measuring the grey levels of each pixel for different models ofhandwritten figures. Each probability p(Pix[i]/CHIFFRE) can be definedby a histogram (with 16 columns) normalized according to the Laplacelaw.

The recognition of a figure comprises a first phase of measurement ofthe grey level of each pixel. In a second phase, a representation of theprobability distribution of the figures is constructed based on formula(5) and on the method of the present invention, knowing the grey levelsof each pixel. The selection of a figure consists of identifying thefigure exhibiting the maximum probability.

3.3. Evaluation of a Transport Cost

A shipping company dispatches by cargo goods from a European port toanother port. The dispatched goods can be of a great variety: foodproducts, medicine, electric appliances, or clothes. Different sorts ofcontainers are used for the storage of the goods in the cargo and in theport of arrival. The containers may be refrigerating and of differentsizes.

The shipping company desires to rapidly determine, in a telephoneconversation, for example, transport expense estimates knowing the portof departure (PortDep) and the port of arrival (PortArr), the type oftransported goods (Mar), the container used (Cont), the client (Cl), andthe month (M) in which the transport will occur. These parameters,previously input on determination of the estimate, form the measurementparameters of the transport system.

Further, the company has in its possession a whole set of informationespecially relative to the container preparation time in the Europeanport of departure (TdP), the shipping time (TdTM) (outward or back, thecontainers are full on the outward trip and empty on the way back), thewaiting time of the container in the port of arrival (TdA), the time ofcontainer unloading at the client's (TdDC), the container reconditioningtime when back in Europe (TdRE), the times being counted in days.

Similarly, information is available relating to the daily cost of therenting of a container (CdLJ), the daily cost of immobilization of acontainer for its reconditioning (CdIJ), the shipping cost (CdTM), therepair cost of a container (CdR).

The total transport cost (CT) is the sum of the total cost of thecontainer renting (CdLT=CdLJ*(TdP+2*TdTM+TdA+TdDC+TdRE)), of the totalcontainer immobilization cost (CdIT), of the shipping cost(CdTM=CdIT*TdRE), of the cost of the load balancing in the cargo (CdE),and of the cost of a container repair (CdR).

The model of the joint probability distribution of all thepreviously-defined parameters is constructed based on the independentprobability distributions defined for each time parameter (TdP, TdTM,TdA, TdDC, and TdRE), and for each cost parameter (CDLT, CdIT, CdTM,CdE, CdR, CT). The probability values are obtained from a set of dataacquired along the company's lifetime. For example, the probabilitydistributions of the container preparation time in the port of departure(TdP) knowing the nature of the good (Mar) are a gaussian family. Theprobability distributions of the shipping costs (CdTM) knowing the typeof container (Cont), the port of departure (PortDep), the port ofarrival (PortArr), and the transported goods (Mar) are Dirac functions.

Generally, the total transport cost (CT) is desired to be definedwithout detailing the intermediary costs. In this case, there is asingle parameter (or specific parameter) to determine: the total cost(CT). To rapidly provide a total cost, a representation of theprobability distribution of the possible total costs CT is constructedaccording to the method of the present invention, knowing themeasurement parameters (PortDep, PortArr, Mar, Cont, Cl, and M). Thevendor first wants to know what the maximum cost is, for example, 2,000euros. He then establishes a first estimate by possibly taking a 10%margin with respect to the maximum cost, then offers 2,200 euros. In thecase where the client does not accept this price, the vendor can thenestimate the average cost or the cost range containing for example 90%of the possible cost values. The average cost can easily be calculatedby dividing intermediary normalization constant Zi by the number ofpossible total costs. The vendor will then establish a second estimateby taking a margin that may be smaller with respect to the average costor with respect to one of the costs of the cost range.

The established estimate may also detail all the costs, in which casethe measurement control parameters of the system are (CdLT, CdIT, CdTM,CdE, CdR). The total cost is then calculated based on the retained costcombination.

This example of application shows that based on a representation, thecombination of maximum probability can easily be determined, the averagevalue and the standard deviation of the values of a parameter can becalculated, and one of the combinations exhibiting a given probabilitycan be selected. The method of the present invention thus enables easilyimplementing several selection criteria.

Of course, the present invention is likely to have various alterations,modifications, and improvements which will readily occur to thoseskilled in the art. In particular, it will be within the abilities ofthose skilled in the art to define the branch ramification method mostadapted to the studied system. Similarly, it will be within theabilities of those skilled in the art to define new criteria of theselection of a combination based on the tree-shaped representation ofthe probability distribution.

1. A method for determining the value to be given to a set of specificparameters of a system based on the values of a set of measurementparameters of this system, where each of the parameters can take afinite number of values, the system being associated with a means forproviding a probability value for any combination of values of thespecific parameters, said probability value being all the greater as theselection of the considered combination is pertinent knowing the valueof the measurement parameters, the method comprising the steps of:noting down the value of each measurement parameter; constructing atree-shaped representation of the probability distribution of all thepossible combinations of values of the specific parameters correspondingto the noted down values, the set of combinations, forming a firstbranch, being divided into several subsets of combinations, formingsecond branches, each subset gathering combinations having closespecific parameter values, where each second branch can similarly divideinto several third branches and so on, a probability value beingassigned to each branch, this probability value being that obtained forone of the combinations of the considered branch or for one of thecombinations of one of the branches from which the considered branchoriginates; selecting according to a predefined selection criterion oneof the combinations of values of the specific parameters based on therepresentation of the previously-constructed tree-shaped probabilitydistribution.
 2. The method of claim 1, wherein the branches resultingfrom the division of a same branch are at the number of two and containthe same number of combinations, the first branch dividing in two secondbranches, where each second branch can divide in two third branches andso on.
 3. The method of claim 2, wherein the division of a branch in twobranches comprises the steps of: a) selecting a combination differentfrom the combinations having already been used to define the probabilityvalue of the existing branches and calculating the probability of thisselected combination; b) dividing the so-called “parent” branchcontaining the selected combination in two so-called “child”combinations; and in the case where the selected combination and the“parent” combination used to define the probability value of the parentbranch belong to the same child branch, assigning to the two childbranches the probability value of the parent branch and dividing thechild branch containing the selected combination by resuming the methodat step b), this child branch becoming the parent branch, and in thecase where the selected combination and the parent combination do notbelong to the same child branch, assigning the probability value of theselected combination to the child branch containing the selectedcombination and assigning the probability value of the parentcombination to the other child branch.
 4. The method of claim 1, whereinthe selection criterion consists of selecting one of the combinationsexhibiting the maximum probability.
 5. The method of claim 2, whereinthe selection of a combination consists of implementing the recursivemethod comprising the steps of: a) randomly selecting a number p rangingbetween 0 and 1; b) calculating the sum of the probability valuesassigned to the two so-called child branches resulting from the divisionof the first branch, and calculating for each child branch a newprobability value equal to the ratio between the probability valueassigned to this child branch and the calculated sum; c) defining twocontiguous probability intervals between 0 and 1, the first intervalbeing associated with a first child branch, the second interval beingassociated with the second child branch, the first interval ranging from0 to and including the probability value of the first child branch andthe second interval ranging from the probability value to 1; d)identifying in which interval number is to be found and selecting thechild branch associated with this interval, and in the case where theselected child branch ramifies into other branches, resuming therecursive method at step a), the first branch being replaced with theselected child branch, otherwise e) selecting one of the combinations ofthe selected child branch.
 6. The method of claim 1, wherein theselection criterion consists of selecting one of the combinations havinga probability value which is predetermined or ranging between two givenprobability values.
 7. The method of claim 1, wherein the probabilityvalues assigned to each branch are not normalized and can be greaterthan one.
 8. The method of claim 7, wherein a weighting is assigned toeach branch, the weighting of the branches of the last ramificationsbeing equal to the product of the probability value assigned to thisbranch and of the number of combinations of this branch, the weightingof the other branches being equal to the sum of the weightings of thebranches originating from the considered branch and being on the nextramification level.
 9. The method of claim 8, wherein the probabilityvalue assigned to each branch can be normalized, the normalizedprobability value of a branch being obtained by dividing the probabilityvalue of this branch by the weighting assigned to the first branch ofthe tree.
 10. The method of claim 3, wherein the selection of acombination is performed by implementing a method generatingcombinations having high probability values.
 11. The method of claim 1,wherein the representation of the probability distribution of all thecombinations is memorized and may be subsequently refined by thecreation of additional branches, or may be simplified by the suppressionof certain branches.
 12. The method of claim 1, wherein the number ofvalues likely to be taken by a parameter is artificially increased, theprobability value of a combination of values of control parameters,among which at least a value of one of the parameters corresponds to anadded value, is zero.